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A Type II Error is when the null hypothesis (H0) is actually false, but we fail to reject it.
Scenario: The Delta Apple Pi chapter at Crammer Nation University claims that their brothers get on average 25 Tinder matches per day. You have a hunch that their daily Tinder matches are actually lower than that, so you collect a random sample of 35 Delta Apple Pi brothers' daily Tinder matches. You measure a mean of 23.5 daily matches with a standard deviation of 5.7 matches. Provide support for your claim using a hypothesis test with an alpha level of 0.05.
The null states that Delta Apple Pi gets an average 25 Tinder matches per day.
So if we fail to reject the null when we shouldn't have...
Type II Error ➡️ We wrongly suggest that Delta Apple Pi is correct about their average Tinder matches... when they're actually not! They're actually lying about how much game they have! (They actually have less than 25 average Tinder matches per day!)
The probability of committing a Type II Error is your beta level (β), which is essentially the "statistical power" of the hypothesis test.
It's essentially the "threshold" that you're comfortable accepting to accept the null when it's actually false (a.k.a. Type II Error).
